Rule 1: Multiply by 2, then add 1/3 starting from 1. Rule 2: Add 1/2, then multiply by 4 starting from 0. What is the fourth ordered pair using the two sequences

(10 1/3, 42)

Step-by-step explanation:

a1 = 1

a2 = a1×2 + 1/3 = 2 1/3

a3 = a2×2 + 1/3 = (a1×2 + 1/3)×2 + 1/3 = a1×4 + 2/3 + 1/3 =

= 4 + 3/3 = 5

a4 = a3×2 + 1/3 = ... = 10 1/3

b1 = 0

b2 = (b1 + 1/2)×4 = (0 + 1/2)×4 = 1/2 × 4 = 2

b3 = (b2 + 1/2)×4 = ((b1 + 1/2)×4 +1/2)×4 = 16×b1 + 16/2 + 4/2=

= 16/2 + 4/2 = 8 + 2 = 10

or (to check we made no mistake)

= (2 + 1/2)×4 = 8 + 2 = 10. => all ok, no mistake

b4 = (b3 + 1/2)×4 = ... = (10 + 1/2)×4 = 40 + 2 = 42

so, the fourth ordered pair (= the fourth elements of each sequence) is therefore (10 1/3, 42)

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

sure i'm up for it

step-by-step explanation: